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Orbital angular momentum at small x

  • Yuri V. KovchegovEmail author
Open Access
Regular Article - Theoretical Physics
  • 42 Downloads

Abstract

We determine the small Bjorken x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of αs ln2(1/x) with αs the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small x, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-x evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-x asymptotics of the quark and gluon OAM distributions in the large-Nc limit:
$$ {L}_{q+\overline{q}}\left(x,{Q}^2\right)=-\Delta \Sigma \left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{\frac{4}{\sqrt{3}}\kern0.5em \sqrt{\frac{\alpha_s\kern0.5em {N}_c}{2\pi }}}, $$
(1a)
$$ {L}_G\left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{\frac{13}{4\sqrt{3}}\kern0.5em \sqrt{\frac{\alpha_s\kern0.5em {N}_c}{2\pi }}}. $$
(1b)

Keywords

Perturbative QCD Resummation 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsThe Ohio State UniversityColumbusU.S.A.

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